Question

Early statisticians noticed the same shape coming up over and over again in

different distributions so they named it the normal distribution. In a normal distribution, approximately what percent of the data falls within 3 standard deviations of the mean?

Answer 1

In a normal distribution, more than 99 percent of the data falls within three standard deviations of the mean, as described by the Empirical Rule, applicable only to bell-shaped, symmetric distributions.

Step-by-step explanation:

In a normal distribution, it is known that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent falls within two standard deviations, and more than 99 percent falls within three standard deviations. This is encapsulated by the Empirical Rule, which is a statistical rule stating the percentage of values that lie within a band around the mean in a bell-shaped, symmetric distribution.

It is important to recognize that the Empirical Rule is only applicable to distributions that are perfectly bell-shaped and symmetric. The normal distribution is considered the most important of all probability distributions because it models many natural phenomena and measurement errors.